Help me choosing module/course

[mathsnerd2]

Main Question or Discussion Point

Algebra 5

DecisionProblemsinGroupTheory(L24)................. .............5
LieAlgebrasandRepresentationTheory(M24)............ ...............5
ModularRepresentationsofFiniteGroups(L24).......... ................6
Calculusandalgebra(L24)............................ ..........8
Representationsof?nitegroupsofLietype(L24)......... .................8
CommutativeAlgebra(M24)............................ .........9
Non-commutativealgebras(L24)....................... ............9
VonNeumannAlgebras(L24)............................ .........10

Analysis 12

TopologicalGroups(L24)............................. ..........12
TopicsinIn?niteGroups(M16)......................... ...........12
AnalysisontheDiscreteHypercube(L24)— Non–Examinable .................13
IntroductiontoFunctionalAnalysis(M24).............. ................14
ComplexDi?erentialEquations(L24)................... .............15
Ellipticpartialdi?erentialequations(M24)........... ..................15

Combinatorics 17

Combinatorics(M16)................................. .........17
CombinatorialProbability(L16)...................... .............17
HypergraphGames(E8)— Non–Examinable ..........................18
ArithmeticCombinatorics(M16)....................... ............18

GeometryandTopology 19

TheX-raytransformingeometryanddynamics(L24)........ ...............19
AlgebraicTopology(M24)............................. ..........20
Di?erentialGeometry(M24)........................... ..........20
SpectralGeometry(L24).............................. .........21
AlgebraicGeometry(M24)............................. .........22
ComplexManifolds(L24).............................. .........22
AlgebraicGroups(M24)............................... .........24
FibreBundles(L16).................................. ........24
AlgebraicCycles(L24)............................... ..........25

Logic 26

CategoryTheory(M24)................................ ........26
SetTheoryandLogic(L24)............................. .........27

NumberTheory 29

EllipticCurves(L24)................................ ..........29
LocalFields(M16)................................... ........29
ErgodicTheory(L24)................................. ........30
TheIwasawatheoryofellipticcurveswithcomplexmultiplication(L24).............31
AlgebraicNumberTheory(M16)......................... ..........31
ModularFormsandAutomorphicForms(L24)............... ............32
Non-abelianLubin-Tatetheory(M24)— Non–Examinable ...................32

Probability 3

AdvancedProbability(M24)........................... ..........3
StochasticNetworks(L24)............................ ...........3
StochasticLoewnerEvolutions(L16)................... ..............3
StochasticCalculusandApplications(L24)............. ................3

ParticlePhysics,QuantumFieldsandStrings 46

QuantumFieldTheory(M24)............................ .........46
SymmetryandParticlePhysics(M24).................... ............47
StatisticalFieldTheoryandApplications(M24)......... .................48
AdvancedQuantumFieldTheory(L24).................... ...........49
StringTheory(L24).................................. ........49
SupersymmetryandExtraDimensions(L24)............... .............50
StandardModel(L24)................................. ........51
SolitonsandInstantons(E16)......................... ............52
Supergravity(E16).................................. .........53
3

QuantumInformationandQuantumFoundations 54

IntroductiontoQuantumComputation(M16).............. .............54
QuantumInformation,EntanglementandNonlocality(M16). ..................55
PhilosophyofClassicalandQuantumMechanics(M12,L12).. .................55
MathematicalAspectsofQuantumInformationTheory(L24). ..................56
QuantumControl(L16)................................ ........57

RelativityandGravitation 59

Cosmology(M24)..................................... .......59
GeneralRelativity(M24)............................. ..........61
AdvancedCosmology(L16)............................. .........62
ApplicationsofDi?erentialGeometrytoPhysics(L24).... ...................63
BlackHoles(L24).................................... .......64
QuantumCosmology(E16).............................. ........65
IntroductionToTwistorTheory(E16)................... ............66

Astrophysics 67

AstrophysicalFluidDynamics(M24).................... .............67
StructureandEvolutionofStars(M24).................. .............68
AccretionDiscs(L16)................................ .........68
Galaxies(L24)...................................... .......69
PhysicalCosmology(L24)............................. ..........70
StellarandPlanetaryMagneticFields(L24)............. ................71

I am interested in differential geometry, group theory, a bit of quantum mechanic, some algebra, complex analysis and topology.

So right now I can't decide what area I want to major in? How do you guys decide what area to specialize?

What subject I should choose so that I can still keep in touch with my favorite topics (differential geometry, group theory, a bit of quantum mechanic, some algebra, complex analysis and topology) ?

Please help me I am clueless.

I only allowed to take 10 course from the list above and hopefully the course that I choose will be useful in my research for PhD ( still haven't decide what topic).

Thank you for your help. :)

 

[PowerIso]

From teaching classes and becoming exposed to the stuff you are interested in. I picked Combinatorics and Game Theory for my specialization because it was something I under innately. I love talking about the subject and all the many applications. It also seems like every day people also enjoy talking about the implication game theory results imply. It extremely interesting and fun for me.

However, to get to that point, it took a lot of work. At first, I thought maybe dynamics, but I didn't like how tedious it was. Then I thought, why not analysis, but it hurts my head to think about analysis for to long. Then I thought why not topology? Again, it hurts my head to much. In the end, it took me figuring out what I enjoyed less to figure out what I really did truly enjoy.

I hope that made sense.

 

[mgiddy911]

I can hardly understand you post however...

You don't major in Diff. Geometry, group theory or even QM

You major in Math or Physics, possibly a bit more specialized but with not much difference something like theoretical physics or a dual degree physics +maths

Later in grad school you begin to specialize if you choose to do p.h.d or some kind of thesis based MS.

How far along are you in your studies? That would help us help you. Are you doing you phd currently? Really you should consult your dept. as far as having trouble picking a topic for a phd. There is only so much we can suggest in that regard, ie. we can't tell you, You Should do you PHD on X, Y or Z.